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ECE 2300 – Final Exam
May 3, 2006
Keep this exam closed until you
are told to begin.
1. This exam is closed book, closed notes. You may use one 8.5” x 11”
crib sheet, or its equivalent.
2. Show all work on these pages. Show all work necessary to complete
the problem. A solution without the appropriate work shown will receive no
credit. A solution that is not given in a reasonable order will lose credit.
Clearly indicate your answer (for example by enclosing it in a box).
3. It is assumed that your work will begin on the same page as the
problem statement. If you choose to begin your work on another page, you
must indicate this on the page with the problem statement, with a clear
indication of where the work can be found. If your work continues on to
another page, indicate clearly where your work can be found. Failure
to indicate this clearly will result in a loss of credit.
4. Show all units in solutions, intermediate results, and figures. Units in
the exam will be included between square brackets.
5. Do not use red ink. Do not use red pencil.
6. You will have 180 minutes to work on this exam.
1. ________________/10
2. ________________/18
3. ________________/12
4. ________________/24
5. ________________/18
6. ________________/18
Total = 100
ECE 2300 – Final Exam – May 3, 2006 – Page 2
1. {10 Points} A number (n) of identical devices, consisting of a voltage source
E0 and a resistor R=1[k], are connected in parallel, and then connected in parallel
with the resistor Rp=90[], as shown in Figure 1. If an ammeter with a meter
resistance Rm= 1[] is connected in to the circuit at point G, find the number of
devices n that must be connected in parallel so that the magnitude of the error of
the current measurement is not bigger than 1%. Your solution should be
expressed as an inequality.
Figure 1.
ECE 2300 – Final Exam – May 3, 2006 – Page 3
2. {18 Points} For the given circuit, use the node-voltage method to write a
complete set of independent equations that could be used to solve this circuit. Do
not simplify the circuit. Do not attempt to solve or simplify your equations.
Define all variables.
2[V]
21[]
22[]
+
-
+
iX
4[V]
3[A]
-
+
24[]
-
+
10vX
11[]iX
29[]
+ v
W
iQ
+
-
23[]
-
vQ
13[]iQ
+
25[]
34[]
-
+
26[]
12vW
28[]
30[]
33[]
27[]
31[]
vX
5[A]
-
14vQ
+
+
-
32[]
ECE 2300 – Final Exam – May 3, 2006 – Page 4
3. {12 Points} The resistor R2 has been added to a multi-range voltmeter with 3
voltage ranges, 5[V], 50[V], and 100[V]. An analog voltmeter, with three ranges
on its display, is used in this multi-range meter. The resistor R2 was added
between the 50[V] terminal and the Common terminal. Find the value of R2 so
that the meter will read 80[V] on the 100[V] scale when connected to a 135[V]
voltage source as shown below.
multi-range voltmeter
100[V]
R1
50[V]
+
10[k]
135[V]
5[V]
V
Analog
Voltmeter
Common
R2
ECE 2300 – Final Exam – May 3, 2006 – Page 5
4. {24 Points} In the circuit below, switch SWA was open and switch SWB was
closed for a long time before t = 0. Then, at t = 0, switch SWA closed. After that,
15[s] later, switch SWB opened. Find iX(20[s]).
SWA
t=0
56[k] iX(t)
3.3[k]
SWB
+
+
-
vS1 =
9[V]
15[k]
-
+
LX =
27[mH]
t = 15[s]
-
vS3 =
75[k]iX
vS2 =
12[V]
ECE 2300 – Final Exam – May 3, 2006 – Page 6
5. {18 Points} In Figure 1, the device is shown with two terminals A and B. The
measured voltage vAB(t) and current id(t) are shown in the Figure 2.
a) Find an appropriate model for this device. This model can be obtained
using the combination of two basic circuit elements.
b) Find the Real, Reactive and Apparent power absorbed by this device.
Figure 1.
time / [s]

0



3.14
4.71
6.28


10
voltage [V] / current [A]
5
3.53
0
-5
t=0.39 [s]
-10
0.00
1.57
time / [s]
Figure 2.
7.85
9.42
voltage
current
ECE 2300 – Final Exam – May 3, 2006 – Page 7
6. {18 Points} In the circuit shown below, a voltage source provides a sinusoidal
voltage to three loads. This system is in steady state, and operates at a frequency
of 60[Hz]. It is known that:
Load 1 absorbs 600[W] and delivers 500[VAR].
Load 2 absorbs 750[VA] with a leading power factor of 0.7.
Load 3 absorbs 80015[VA].
Find iX(t) for this system.
Ix,rms
Vs,rms =
+
150 0° [Vrms]
-
Load 1
Load 2
Load 3
ECE 2300 – Final Exam – May 3, 2006 – Page 8
Solutions:
1. {10 Points} A number (n) of identical devices, consisting of a voltage source
E0 and a resistor R=1[k], are connected in parallel, and then connected in parallel
with the resistor Rp=90[], as shown in Figure 1. If an ammeter with a meter
resistance Rm= 1[] is connected in to the circuit at point G, find the number of
devices n that must be connected in parallel so that the magnitude of the error of
the current measurement is not bigger than 1%. Your solution should be
expressed as an inequality.
Figure 1.
ECE 2300 – Final Exam – May 3, 2006 – Page 9
ECE 2300 – Final Exam – May 3, 2006 – Page 10
ECE 2300 – Final Exam – May 3, 2006 – Page 11
ECE 2300 – Final Exam – May 3, 2006 – Page 12
2. {18 Points} For the given circuit, use the node-voltage method to write a
complete set of independent equations that could be used to solve this circuit. Do
not simplify the circuit. Do not attempt to solve or simplify your equations.
Define all variables.
ECE 2300 – Final Exam – May 3, 2006 – Page 13
ECE 2300 – Final Exam – May 3, 2006 – Page 14
3. {12 Points} The resistor R2 has been added to a multi-range voltmeter with 3
voltage ranges, 5[V], 50[V], and 100[V]. An analog voltmeter, with three ranges
on its display, is used in this multi-range meter. The resistor R2 was added
between the 50[V] terminal and the Common terminal. Find the value of R2 so
that the meter will read 80[V] on the 100[V] scale when connected to a 135[V]
voltage source as shown below.
ECE 2300 – Final Exam – May 3, 2006 – Page 15
4. {24 Points} In the circuit below, switch SWA was open and switch SWB was
closed for a long time before t = 0. Then, at t = 0, switch SWA closed. After that,
15[s] later, switch SWB opened. Find iX(20[s]).
ECE 2300 – Final Exam – May 3, 2006 – Page 16
ECE 2300 – Final Exam – May 3, 2006 – Page 17
ECE 2300 – Final Exam – May 3, 2006 – Page 18
5. {18 Points} In Figure 1, the device is shown with two terminals A and B. The
measured voltage vAB(t) and current id(t) are shown in the Figure 2.
a) Find an appropriate model for this device. This model can be obtained
using the combination of two basic circuit elements.
b) Find the Real, Reactive and Apparent power absorbed by this device.
Figure 1.
time / [s]

0



3.14
4.71
6.28


10
voltage [V] / current [A]
5
3.53
0
-5
t=0.39 [s]
-10
0.00
1.57
time / [s]
Figure 2.
7.85
9.42
voltage
current
ECE 2300 – Final Exam – May 3, 2006 – Page 19
ECE 2300 – Final Exam – May 3, 2006 – Page 20
ECE 2300 – Final Exam – May 3, 2006 – Page 21
6. {18 Points} In the circuit shown below, a voltage source provides a sinusoidal
voltage to three loads. This system is in steady state, and operates at a frequency
of 60[Hz]. It is known that:
Load 1 absorbs 600[W] and delivers 500[VAR].
Load 2 absorbs 750[VA] with a leading power factor of 0.7.
Load 3 absorbs 80015[VA].
Find iX(t) for this system.
Ix,rms
Vs,rms =
+
150 0° [Vrms]
-
Load 1
Load 2
Load 3
ECE 2300 – Final Exam – May 3, 2006 – Page 22